Could you check your app settings on the tablet to make sure your automatic log out options are set to your preference?
Select the Vault Menu icon in the upper-left of the screen, then go to Settings > Security.
Check these settings and set them to your preference: Lock LastPass automatically: allows you to set when LastPass will lock itself if sent to the background or if the screen is turned off. Accessing LastPass again will require either your Master Password or a PIN code. The sub options allow you to set a PIN code and modify the Reprompt Timer. Log out when app is idle: allows you to set a time limit to ensure that your LastPass Password Manager app logs off after X minutes of LastPass being logged in, but in the background of your device.